Blender hangs for a minute
I marked the first correct answer as accepted. This is indeed a problem with network drives. But it seems I found a workaround, so I post it here.

The workaround removes all network drives from Blender, so it doesn't hang while trying to access them. It will also kill the possibility to save / load files to network drives in Blender. I do not need this feature so this is fine for me.

Before you start with this, try running Blender as Administrator (right click on its shortcut and choose 'Run as administrator'. I heard it might remove network drives on some systems. It did not work for me however. Verify by going to File> Open in Blender and see if network drives are still there.

Steps which resolved this for me:


Create a new user in Windows. I named it "Blender". Set administrative rights to it so it can access all the files and create a valid, strong password for it so nobody will login to the PC with it.
Create a shortcut somewhere (ie. desktop) to start blender. It can be a copy of the blender shortcut which is in the start menu (Start -> find blender -> right click -> copy, then right click on desktop -> paste).
Change the target of this shortcut, so it is not:

C:\Program Files\Blender Foundation\Blender\blender.exe 

but instead:

runas.exe /savecred /user:Blender "C:\Program Files\Blender Foundation\Blender\blender.exe"

If your path to blender.exe is different, adjust accordingly. If you username is different than Blender, also change it.
Now double clicking new shortcut will start Blender on this different user account. At first run it will ask for the password - enter the password set for the Blender user.
Blender will start instantly, because this new user doesn't have any network drives mapped.
If caring for look, you can change the icon for the shortcut, because now it doesn't look like anything Blender like. Just find 'Change Icon' button in shortcut properties, navigate to:

C:\Program Files\Blender Foundation\Blender\blender.exe 

and set a proper icon.
Blender is now like fresh install without user settings. You can copy your current settings by copying:

C:\Users\\AppData\Roaming\Blender Foundation\Blender\2.76\config\userpref.blend

to

C:\Users\Blender\AppData\Roaming\Blender Foundation\Blender\2.76\config\userpref.blend

This path might different on your system or different Blender version. Do the same with other files in this folder: 'bookmarks.txt' and 'recent-files.txt'. If you have more files there, consider them as well (I only had those).